The best of ideas is hurt by uncritical acceptance and thrives on critical examination.
Interpretation
Ideas flourish under scrutiny and suffer from blind acceptance.
George Polya emphasizes the importance of critical thinking in the evaluation of ideas. Accepting ideas without question can lead to stagnation, while subjecting them to rigorous examination can enhance understanding and innovation.
In practice
During a team meeting, I reminded everyone that the best solutions come from questioning our assumptions.
Pedantry and mastery are opposite attitudes toward rules. To apply a rule to the letter, rigidly, unquestioningly, in cases where it fits and in cases where it does not fit, is pedantry. [...] To apply a rule with natural ease, with judgment, noticing the cases where it fits, and without ever letting the words of the rule obscure the purpose of the action or the opportunities of the situation, is mastery.
If you wish to learn swimming you have to go into the water and if you wish to become a problem solver you have to solve problems.
To teach effectively a teacher must develop a feeling for his subject; he cannot make his students sense its vitality if he does not sense it himself. He cannot share his enthusiasm when he has no enthusiasm to share. How he makes his point may be as important as the point he makes; he must personally feel it to be important.
Mathematics is not a spectator sport!
Mathematics is being lazy. Mathematics is letting the principles do the work for you so that you do not have to do the work for yourself
In order to translate a sentence from English into French two things are necessary. First, we must understand thoroughly the English sentence. Second, we must be familiar with the forms of expression peculiar to the French language. The situation is very similar when we attempt to express in mathematical symbols a condition proposed in words. First, we must understand thoroughly the condition. Second, we must be familiar with the forms of mathematical expression.
That is the challenge Companion. To take what has happened to you and learn from it. Nothing is quite so destructive as pity, especially self-pity. No event in life is so terrible that one cannot rise above it.
A hair shirt does not always render those chaste who wear it.
There was once a fiddler who played so beauitully that everybody danced. A deaf man who could not hear the music considered them all insane. Those who are with Jesus in suffering hear this music to which other men are deaf. They dance and do not care if they are considered insane.
Do not let it be your aim to be something, but to be someone.
What suffering has taught me is the uselessness of suffering.
The willow which bends to the tempest, often escapes better than the oak which resists it; and so in great calamities, it sometimes happens that light and frivolous spirits recover their elasticity and presence of mind sooner than those of a loftier character.
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